A calibrated fully interpretable fuzzy classifier via Vapnik-Chervonenkis-dimension minimization learning

Yuchen Li, Fu-lai Chung, Yusuke Nojima, Shitong Wang

Abstract: This study explores a novel calibrated fully interpretable fuzzy classifier for binary classification tasks, where both fully interpretable classification and calibrated outputs are in demand. In structural sense, the proposed fuzzy classifier VCM-FC adopts each fully interpretable fuzzy rule, which is derived directly from the joint mean of the corresponding Gaussian mixture model on the training set, to realize fully interpretable classification. Meanwhile, VCM-FC takes the particularly-designed calibrated decision function on Gaussian mixture model’s joint mean and joint variance for each input sample to guarantee each calibrated output. In training sense, based on the derived Vapnik–Chervonenkis-dimension upper bound of VCM-FC on the designed calibrated decision function, the learning objective of VCM-FC is proposed, and accordingly, the training of VCM-FC with the guarantee of enhanced generalizability can be well accomplished by optimizing the proposed learning objective with an available linear programming solver. Experimental results on 14 benchmarking datasets validate VCM-FC’s effectiveness in terms of testing performance, training speed, and full interpretability. Particularly, when VCM-FC with 20 fully interpretable fuzzy rules works for a case study about Electricity Pricing, it reaches average testing accuracy of 76.01%, which is better than the comparative fuzzy classifiers with the same number of fuzzy rules.